119edo: Difference between revisions

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== Theory ==

It is ~~notable for offering as many as four different options for fifths:~~

119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.

~~68 steps: 7edo superflat fifth: 17 17 17 17 17 17~~ 17

Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit.

~~69 steps: Approximation~~ of ~~2/7 comma meantone: 19 19 19 12 19 19 19 19 12~~

=== Odd harmonics ===

=== Subsets and supersets ===

Since 119edo factors as {{Factorization|119}}, it contains [[7edo]] and [[17edo]] as a subset. Hence it supports circles of fifths of those respective equal temperaments.

~~70 steps: 17edo sharp fifth (patent): 21 21 7 21 21 21 7, 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1~~

== Scales ==

~~71 steps~~: Approximation of half comma eventone: 23 23 2 23 23 23 2, 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2

* Approximation of 2/7 comma meantone: 19 19 19 12 19 19 19 19 12

* Approximation of half comma eventone: 23 23 2 23 23 23 2, 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2

~~=== Harmonics ===~~

~~{{Harmonics in equal|119}}~~

[[Category:Equal divisions of the octave|###]]

@@ Line 2: / Line 2: @@
 {{EDO intro|119}}
 == Theory ==
-It is notable for offering as many as four different options for fifths:
+edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.
-steps: 7edo superflat fifth: 17 17 17 17 17 17 17
+Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit.
-steps: Approximation of 2/7 comma meantone: 19 19 19 12 19 19 19 19 12
+=== Odd harmonics ===
+{{Harmonics in equal|119|columns=20}}
+=== Subsets and supersets ===
+Since 119edo factors as {{Factorization|119}}, it contains [[7edo]] and [[17edo]] as a subset. Hence it supports circles of fifths of those respective equal temperaments.
-steps: 17edo sharp fifth (patent): 21 21 7 21 21 21 7, 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1
+== Scales ==
-steps: Approximation of half comma eventone: 23 23 2 23 23 23 2, 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2
+* Approximation of 2/7 comma meantone: 19 19 19 12 19 19 19 19 12
+* Approximation of half comma eventone: 23 23 2 23 23 23 2, 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2
-=== Harmonics ===
-{{Harmonics in equal|119}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->